Quantum Annealing with Qubit-Resonator Systems for Simultaneous Optimization of Binary and Continuous Variables

TL;DR

This paper introduces a hybrid quantum annealing approach using qubits and resonators to efficiently optimize problems with both binary and continuous variables, addressing limitations of traditional binary-only quantum annealing.

Contribution

It proposes a novel hybrid quantum annealing framework that directly handles continuous variables alongside binary ones, reducing qubit requirements and expanding problem applicability.

Findings

Numerical simulations demonstrate the feasibility of the hybrid approach.

The method effectively minimizes hybrid cost functions.

Potential for more efficient quantum optimization of complex problems.

Abstract

Quantum annealing is a method developed to solve combinatorial optimization problems by utilizing quantum bits. Solving such problems corresponds to minimizing a cost function defined over binary variables. However, in many practical cases, the cost function may also involve continuous variables. Representing continuous variables using quantum bits requires binary encoding, which demands a large number of qubits. To overcome this limitation, an approach using quantum resonators has been proposed, enabling the direct handling of continuous variables within the quantum annealing framework. On the other hand, certain optimization problems involve both binary and continuous variables simultaneously, and a quantum annealing method capable of efficiently solving such hybrid problems has not been established. Here, we propose a quantum annealing method based on a hybrid system composed of qubits and resonators, aiming to minimize cost functions that contain both binary and continuous variables. We present a general framework for hybrid quantum annealing using such systems, and investigate its feasibility and effectiveness through numerical simulations.